How are aliens related to math? The answer is: in every possible way!
From science fiction, to popular culture, to UFO organizations, and even a famous jerky shop half way between Los Angeles and Las Vegas named Alien Fresh Jerky, extraterrestrial life pervades our imagination. The question is: if they are out there, where are they?
This is the foundation of the Fermi Paradox, formulated by Enrico Fermi – one of the most celebrated nuclear physicists of our time – which states the apparent contradiction between high estimates of the probability of the existence of extraterrestrial civilization and humanity’s lack of contact with, or evidence for, such civilizations.
Enrico Fermi is also the architect of “Fermi Estimations,” which is designed to solve complex dimensional analysis problems with simple math calculations. A classical Fermi question would be, “How many piano tuners are there in New York City?”
To solve this puzzle, one may make the following simple estimates:
- Approximately how many people are in New York City? 8,000,000
- Does every individual own a piano? No
- Would it be reasonable to assert that “individuals don’t tend to own pianos, families do? Yes
- About how many families are there in a city of 8 million people? Perhaps there are 1,500,000 families in NYC.
- Does every family own a piano? No. Perhaps one out of every five does. That would mean there are about 300,000 pianos in NYC.
- How many piano tuners are needed for 300,000 pianos? Some people never get around to tuning their piano; some people tune their piano every month. If we assume that “on the average” every piano gets tuned once a year, then there are 300,000 “piano tunings” every year.
- How many piano tunings can one piano tuner do? Let’s assume that the average piano tuner can tune 3 pianos a day. Also assume that there are 200 working days per year. That means that every tuner can tune about 600 pianos per year.
- How many piano tuners are needed in NYC? The number of tuners is approximately 300,000/600 or 500 piano tuners.
Now, let’s do an alien question: in the Soyuz TMA-18M spacecraft, what is the maximum number of Alien Fresh Jerky can astronauts eat before finding an alien? Assuming the estimation of Search for Extraterrestrial Intelligence (SETI) Program is correct, which is 20 years, and that Alien Fresh Jerkies are their only source of food.
- How many astronauts in the Soyuz TMA-18M spacecraft? 6
- How many calories does an astronaut consume in spacecraft per day? 2500. 6 astronauts: 15,000
- Jerky calories? 50 calories per piece, 200 mg sodium
- Max sodium per day? About 3,000 mg
- Max Jerky per day based on sodium intake? 3000/200= 15 pieces
- Total calories for 15 pieces of jerky? 50×15=750 calories
- How many days in 20 years? 365×20= 7300 days
- What is the maximum number of jerky will be eaten in order for astronauts to survive the trip? 15x6x7300= 657,000 pieces
Answer: assuming Alien Fresh Jerky is the only source of food on the space shuttle, the maximum jerkies Soyuz TMA-18M astronauts can consume to stay alive during their 20 years travel is 657,000.
Even though many Fermi Estimations cannot be verified or implemented in daily life, it is a great exercise to deepen our understanding of the world. Fermi Estimations require participants to think up and answer questions using math and science skills, as well as using practical knowledge accumulated through our lived experience. It is a great way to contemplate the scale of our world and put us in perspective.
Can you think of any Fermi Questions? Send it over, and let’s solve it together!
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This post is part of the Hoagies’ Gifted Blog Hop: March Math-ness!. Please click the image below to keep on hopping!